It is well known to make fiber-reinforced structures and building materials from water-curable inorganic binders, such as cement and calcium silicate, and asbestos fibers. The use of asbestos fibers, however, has become disfavored due to safety and health concerns. It has been proposed to replace asbestos fibers with natural cellulosic fibers such as softwood fibers, hardwood fibers, and a variety of vegetable fibers such as hemp, flax, and bagasse. While the properties of such fiber-reinforced structures are generally satisfactory, it is desirable to increase the strength and toughness of such structures or otherwise reduce the quantity of fibers needed to attain certain levels of strength and toughness. Accordingly, it is an object of this invention to provide a cellulose fiber-reinforced structure and process for making it wherein cellulose fiber-reinforced structures having improved toughness and strength are obtained relative to prior known cellulose fiber-reinforced structures.